Issue:Invariant intuitionistic fuzzy observables

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Title of paper: Invariant intuitionistic fuzzy observables Author(s): Katarína Čunderlíková     0000-0002-9772-2717 Mathematical Institute, Slovak Academy of Sciences, Stefánikova 49, 814 73 Bratislava, Slovakia cunderlikova.lendelova@gmail.com Published in: Notes on Intuitionistic Fuzzy Sets, Volume 32 (2026), Number 1, pages 1–14 DOI: https://doi.org/10.7546/nifs.32.1.1-14 Download:  PDF (222  Kb, File info) Abstract: The aim of this contribution is showed that a sequence of Cesaro means of intuitionistic fuzzy observables has an invariant limit m-almost everywhere, where m is an intuitionistic fuzzy state. We proved that this limit is an invariant intuitionistic fuzzy observable for a special type of intuitionistic fuzzy observables called P-intuitionistic fuzzy observables. We formulated the modification of the Individual Ergodic Theorem for this case of intuitionistic fuzzy observables. Keywords: Intuitionistic fuzzy observable, Intuitionistic fuzzy state, Almost everywhere convergence, Almost everywhere coincidence, Joint intuitionistic fuzzy observable, Product, Invariant intuitionistic fuzzy observable, Cesaro means, P-intuitionistic fuzzy observable, Individual Ergodic Theorem. AMS Classification: 60A86, 60A10, 60F17, 28D05, 37A30. References: Atanassov, K. T. (1983). Intuitionistic fuzzy sets. VII ITKR Session, Sofia, 20-23 June 1983 (Deposed in Centr. Sci.-Techn. Library of the Bulg. Acad. of Sci., 1697/84) (in Bulgarian). Reprinted: Int. J. Bioautomation, 20(1), S1–S6. Atanassov, K. T. (1999). Intuitionistic Fuzzy Sets: Theory and Applications. Physica Verlag, New York. Atanassov, K. T. (2012). On Intuitionistic Fuzzy Sets. Springer, Berlin. Čunderlíková, K. (2018). Upper and lower limits and m-almost everywhere convergence of intuitionistic fuzzy observables. Notes on Intuitionistic Fuzzy Sets, 24(4), 40–49. Čunderlíková, K. (2019). m-almost everywhere convergence of intuitionistic fuzzy observables induced by Borel measurable function. Notes on Intuitionistic Fuzzy Sets, 25(2), 29–40. Čunderlíková, K. (2020). A note on mean value and dispersion of intuitionistic fuzzy events. Notes on Intuitionistic Fuzzy Sets, 26(4), 1–8. Čunderlíková, K. (2020). Individual ergodic theorem for intuitionistic fuzzy observables using intuitionistic fuzzy state. Iranian Journal of Fuzzy Systems, 17(5), 13–22. Čunderlíková, K. (2025). Coincidence of intuitionistic fuzzy observables. Notes on Intuitionistic Fuzzy Sets, 31(4), 458-464. Jurečková, M. (2003). The addition to the ergodic theorem on probability MV-algebras with product. Soft Computing, 7, 472–475. Jurečková, M., & Riečan, B. (2005). Invariant observables and the Individual Ergodic Theorem. International Journal of Theoretical Physics, 44, 1587–1597. Lendelová, K. (2006). Conditional IF-probability. Advances in Soft Computing: Soft Methods for Integrated Uncertainty Modelling, 37, Springer, Berlin, Heidelberg, 275–283. Riečan, B. (2006). On the probability and random variables on IF events. Applied Artificial Intelligence, Proc. 7th FLINS Conference, Genova (Ruan, D., et al. (Eds.). 138–145. Riečan, B. (2012). Analysis of fuzzy logic models, Intelligent systems (Koleshko, V. (Ed.). INTECH, 219–244. Riečan, B., & Neubrunn, T. (1997). Integral, Measure, and Ordering. Kluwer Academic Publishers, Dordrecht and Ister Science, Bratislava. Citations: The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.